Only days after teaming up with the Coalition on Senate voting reforms that have increased speculation of an early federal election, Greens leader Richard Di Natale has accused the government of being "shambolic" and divided in its handling of key policy issues.

Senator Di Natale said the Turnbull government would look like it was panicking if it called a double dissolution poll.

It had mishandled the debate on taxation reform, and the Prime Minister Malcolm Turnbull had also failed a key test of leadership by watering down aspects of the controversial Safe Schools policy, Senator Di Natale said.

"The government does look very divided, it looks shambolic at the moment, and to sort of be panicking and running to an early election ... I don't think it would be a good look for them," he told Sky News on Sunday.

Senator Di Natale said Mr Turnbull had "squibbed" the opportunity to stare down critics of the school anti-bullying program.

Education Minister Simon Birmingham unveiled sweeping changes to the program on Friday, saying a review found a number of lessons and content were inappropriate for children.

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"This was an opportunity for the prime minister to finally show a bit of leadership ... (but) he caved in to those very conservative dinosaurs who belong in the last century," Senator Di Natale said.

The support of the Greens was crucial in giving the Coalition the numbers to push the electoral reforms, which passed through the Senate on Friday after a marathon 40-hour debate. The changes are aimed at eliminating elaborate preference-swapping deals that have contributed to micro-party representatives winning seats with as little as 0.5 per cent of the primary vote.

In a double dissolution election, which needs to be held by July 2 and called before May 11, all senators would be up for re-election - and political observers believe most crossbenchers would be wiped out.

On Saturday, two of the affected Senators, Family First's Bob Day and Liberal Democrat David Leyonhjelm, revealed they would launch High Court action over the changes.